statistics: please answer

Question

A researcher is interested in whether students who attend private high schools have higher average SAT scores than students in the general population of high school students. A random sample of 90 students at a private high school is tested and has a mean SAT score of 1,050. The average for public high school students is 1,000 (s 5200).

a.Is this a one- or two-tailed test?

b.What are H0 and Ha for this study?

c.Compute zobt.

d.What is zcv?

e.Should H0 be rejected? What should the researcher conclude?

use α = .05!!!!

Answer 1

This will be a one-sided test.

H₀: μ = 1000

H_A: μ > 1000 (Claim that students who attend private high schools have higher average SAT scores than students in the general population of high school students

n = 90 high school students

X = 1050 (mean SAT score for private high school students)

μ = 1000 (average score for public high school students)

σ = 200

z = (X - μ) / (σ/√n) = (1050 - 1000) / (200/√90) = 50/21.08 ≈ 2.37

Use the z-score table from the Normal Distribution to find the p-value.

P(z > 2.37) = 0.9911

α = 1 - 0.9911 = 0.0089 ≈ 0.01 (1% level of significance)

The critical value for a z-test is 2.3263.

The z-statistic is greater than the critical value, 2.37 > 2.3263.

Therefore, we can reject the null hypothesis. There is sufficient evidence that shows students who attend private high schools have higher average SAT scores than students in the general population of high school students.